Vol. 3, No. 3, 2009

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
The semigroup of Betti diagrams

Daniel Erman

Vol. 3 (2009), No. 3, 341–365
Abstract

The recent proof of the Boij–Söderberg conjectures reveals new structure about Betti diagrams of modules, giving a complete description of the cone of Betti diagrams. We begin to expand on this new structure by investigating the semigroup of such diagrams. We prove that this semigroup is finitely generated, and answer several other fundamental questions about it.

Keywords
Boij–Söderberg Theory, Betti diagrams, Betti tables, minimal free resoultions
Mathematical Subject Classification 2000
Primary: 13D02
Secondary: 13D25
Milestones
Received: 9 November 2008
Revised: 22 January 2009
Accepted: 20 February 2009
Published: 1 May 2009
Authors
Daniel Erman
Department of Mathematics
University of California
Berkeley, CA 94720-3840
United States
http://math.berkeley.edu/~derman